Maximum principles around an eigenvalue with constant eigenfunctions
نویسندگان
چکیده
A class of linear operators L+λI between suitable function spaces is considered, when 0 is an eigenvalue of L with constant eigenfunctions. It is proved that L + λI satisfies a strong maximum principle when λ belongs to a suitable pointed left-neighborhood of 0, and satisfies a strong uniform antimaximum principle when λ belongs to a suitable pointed right-neighborhood of 0. Applications are given to various type of ordinary or partial differential operators with periodic or Neumann boundary conditions. MSC (2000) : Primary 35B50; Secondary 34C25, 35J40, 35L20, 47B60
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